%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV255-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:30:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 14 unt; 2 nHn; 14 RR)
% Number of literals : 40 ( 0 equ; 17 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 48 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(V_U,v_xb(V_U),tc_nat) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_x,V_U,tc_nat) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_xa,V_U,tc_nat) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ) ).
cnf(cls_Nat_Oadd__leE_0,axiom,
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ) ).
cnf(cls_Nat_Oadd__leE_1,axiom,
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_x,v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat)),tc_nat) ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat))))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_xb(X_3)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_xa,v_xb(X_3),tc_nat) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(v_xb(X_3)))]]) ).
cnf(refute_0_2,plain,
( c_in(c_Message_Omsg_ONonce(v_xb(X_3)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(X_3)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(X_3))]]) ).
cnf(refute_0_3,plain,
( ~ c_lessequals(v_xa,v_xb(X_3),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(X_3)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(v_xb(X_3)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ c_lessequals(v_xa,v_xb(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat)),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(subst,[],[refute_0_3:[bind(X_3,$fot(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat)))]]) ).
cnf(refute_0_5,plain,
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat)),tc_nat)
| c_lessequals(V_k,v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat)),tc_nat) ),
inference(subst,[],[cls_Nat_Oadd__leE_0:[bind(V_n,$fot(v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat))))]]) ).
cnf(refute_0_6,plain,
c_lessequals(c_plus(X_6,X_5,tc_nat),v_xb(c_plus(X_6,X_5,tc_nat)),tc_nat),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(c_plus(X_6,X_5,tc_nat)))]]) ).
cnf(refute_0_7,plain,
( ~ c_lessequals(c_plus(X_6,X_5,tc_nat),v_xb(c_plus(X_6,X_5,tc_nat)),tc_nat)
| c_lessequals(X_5,v_xb(c_plus(X_6,X_5,tc_nat)),tc_nat) ),
inference(subst,[],[cls_Nat_Oadd__leE_0:[bind(V_k,$fot(X_5)),bind(V_m,$fot(X_6)),bind(V_n,$fot(v_xb(c_plus(X_6,X_5,tc_nat))))]]) ).
cnf(refute_0_8,plain,
c_lessequals(X_5,v_xb(c_plus(X_6,X_5,tc_nat)),tc_nat),
inference(resolve,[$cnf( c_lessequals(c_plus(X_6,X_5,tc_nat),v_xb(c_plus(X_6,X_5,tc_nat)),tc_nat) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
c_lessequals(c_plus(V_m,V_k,tc_nat),v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat)),tc_nat),
inference(subst,[],[refute_0_8:[bind(X_5,$fot(c_plus(V_m,V_k,tc_nat))),bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_10,plain,
c_lessequals(V_k,v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat)),tc_nat),
inference(resolve,[$cnf( c_lessequals(c_plus(V_m,V_k,tc_nat),v_xb(c_plus(X_9,c_plus(V_m,V_k,tc_nat),tc_nat)),tc_nat) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
c_lessequals(v_xa,v_xb(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat)),tc_nat),
inference(subst,[],[refute_0_10:[bind(V_k,$fot(v_xa)),bind(V_m,$fot(X_13)),bind(X_9,$fot(X_14))]]) ).
cnf(refute_0_12,plain,
c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[$cnf( c_lessequals(v_xa,v_xb(c_plus(X_14,c_plus(X_13,v_xa,tc_nat),tc_nat)),tc_nat) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(subst,[],[refute_0_12:[bind(X_13,$fot(X_15)),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_14,plain,
~ c_lessequals(v_x,v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat)),tc_nat),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X_16,c_plus(X_15,v_xa,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
~ c_lessequals(v_x,v_xb(c_plus(v_x,c_plus(X_15,v_xa,tc_nat),tc_nat)),tc_nat),
inference(subst,[],[refute_0_14:[bind(X_16,$fot(v_x))]]) ).
cnf(refute_0_16,plain,
c_lessequals(c_plus(X_20,X_19,tc_nat),v_xb(c_plus(X_20,X_19,tc_nat)),tc_nat),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(c_plus(X_20,X_19,tc_nat)))]]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(c_plus(X_20,X_19,tc_nat),v_xb(c_plus(X_20,X_19,tc_nat)),tc_nat)
| c_lessequals(X_20,v_xb(c_plus(X_20,X_19,tc_nat)),tc_nat) ),
inference(subst,[],[cls_Nat_Oadd__leE_1:[bind(V_k,$fot(X_19)),bind(V_m,$fot(X_20)),bind(V_n,$fot(v_xb(c_plus(X_20,X_19,tc_nat))))]]) ).
cnf(refute_0_18,plain,
c_lessequals(X_20,v_xb(c_plus(X_20,X_19,tc_nat)),tc_nat),
inference(resolve,[$cnf( c_lessequals(c_plus(X_20,X_19,tc_nat),v_xb(c_plus(X_20,X_19,tc_nat)),tc_nat) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
c_lessequals(v_x,v_xb(c_plus(v_x,c_plus(X_15,v_xa,tc_nat),tc_nat)),tc_nat),
inference(subst,[],[refute_0_18:[bind(X_19,$fot(c_plus(X_15,v_xa,tc_nat))),bind(X_20,$fot(v_x))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( c_lessequals(v_x,v_xb(c_plus(v_x,c_plus(X_15,v_xa,tc_nat),tc_nat)),tc_nat) )],[refute_0_19,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV255-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 18:29:25 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------